Orbitals

Orbitals in chemistry are regions within an atom where electrons are most likely to be found. They are defined by quantum mechanics and can be described in terms of their shapes, sizes, and orientations. Here's a detailed look at orbitals:

1.0Atomic Orbitals and Quantum Numbers 

An atomic orbital is a region around an atom's nucleus where an electron is likely to be found. It comes from solving the Schrödinger equation for the atom, which gives the energy levels and wave functions of the electron. These wave functions are described by quantum numbers and show where an electron is most likely to be.

Quantum numbers are a set of numerical values that describe the unique quantum state of an electron in an atom. They provide important information about the electron's position, energy, angular momentum, and spin. Let’s understand quantum numbers in detail:

1. Principal Quantum Number (n):

• The Principal Quantum Number determines the energy level and size of the electron’s orbital.
• Indicates the main energy level or shell.
• Values are positive integers (1, 2, 3, ...).
• Higher n values correspond to higher energy levels and larger orbitals.

2. Azimuthal Quantum Number (l):

• The azimuthal quantum number, also known as the orbital angular momentum quantum number, defines the shape of the orbital.
• Determines the shape of the orbital.
• Values range from 0 to n−1.

Each value of l corresponds to a specific orbital type:

l=0: s-orbital (spherical shape)

l=1: p-orbital (dumbbell shape)

l=2: d-orbital (cloverleaf shape)

l=3: f-orbital (complex shapes)

3. Magnetic Quantum Number (m_l​):

• The magnetic quantum number describes the orientation of the orbital in space relative to the three axes (x, y, z).
• Specifies the orientation of the orbital in space.
• Values range from −l to +l.
• For example, for l=1 (p-orbitals), m_l can be −1, 0, or +1, corresponding to the three different orientations of p-orbitals.

4. Spin Quantum Number (m_s​):

• The spin quantum number describes the intrinsic spin or angular momentum of the electron.
• Describes the spin of the electron within an orbital.
• Can be ─ 12​ or + 12 .

2.0Types of Orbitals

1. s-Orbitals:

• Spherical in shape.
• Each energy level has one s-orbital (l=0, m_l=0).
• Can hold up to 2 electrons.

2. p-Orbitals:

• Dumbbell-shaped.
• There are three p-orbitals per energy level (for l=1, m_l=−1,0,+1).
• Each p-orbital can hold 2 electrons, so the three p-orbitals can hold a total of 6 electrons.

3. d-Orbitals:

• Cloverleaf or double dumbbell-shaped.
• Five d-orbitals per energy level (for l=2, m_l=−2,−1,0,+1,+2).
• Each d-orbital can hold 2 electrons, so the five d-orbitals can hold a total of 10 electrons.

4. f-Orbitals:

• Complex shapes.
• Seven f-orbitals per energy level (for l=3, m_l=−3,−2,−1,0,+1,+2,+3).
• Each f-orbital can hold 2 electrons, so the seven f-orbitals can hold a total of 14 electrons.

3.0Rules for electron filling in orbitals

The rules for electron filling in orbitals are guided by three main principles: the Aufbau principle, the Pauli exclusion principle, and Hund's rule. Here’s a summary of each:

1. Aufbau Principle:

Electrons occupy the lowest energy orbitals first before filling higher energy orbitals.

The order of filling is determined by the increasing energy levels of the orbitals, often memorized by the sequence:         

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p

2. Pauli Exclusion Principle:

No two electrons in the same atom can have the same set of four quantum numbers (n, l, m_l, m_s).

This means each orbital can hold a maximum of two electrons, and they must have opposite spins (one with +½ and one with -½).

3. Hund's Rule:

When electrons occupy orbitals of the same energy (degenerate orbitals), one electron enters each orbital until all orbitals have one electron with parallel spins.

After each orbital in a subshell is singly occupied, electrons start pairing up with opposite spins.

Example: Filling Order for Carbon (C)

1. Aufbau Principle:

• 1s: 2 electrons
• 2s: 2 electrons
• 2p: 2 electrons (remaining electrons)

2. Pauli Exclusion Principle:

• 1s orbital: 2 electrons (opposite spins)
• 2s orbital: 2 electrons (opposite spins)
• 2p orbitals: 2 electrons in separate orbitals (following Hund's rule)

3. Hund's Rule:

• 2p orbitals: 1 electron in each of the first two 2p orbitals, both with parallel spins
• So, the electron configuration for carbon (C) is 1s² 2s² 2p², following these three rules.

4.0Orbital overlap concept

The orbital overlap concept explains how covalent bonds form when atomic orbitals from different atoms come close enough to interact and share electrons. This overlap can occur in two main ways: sigma (σ) bonds, formed by head-on overlap of orbitals (such as s-s, s-p, or p-p), and pi (π) bonds, formed by the side-by-side overlap of p-orbitals. The strength of a covalent bond is directly related to the extent of orbital overlap; greater overlap results in a stronger bond. This concept is fundamental in understanding molecular bonding, structure, and geometry.

Sigma (σ) bonds, formed by direct end-to-end overlap, are stronger than pi (π) bonds, which have less effective side-by-side overlap. Hybridization, such as sp³ in methane (CH₄), maximizes orbital overlap to form stronger sigma bonds. Molecular geometry is also influenced by orbital overlap, with specific hybridizations like sp in acetylene (C₂H₂) resulting in a linear shape due to optimal overlap along the bond axis.

5.0Importance of Orbitals

• Chemical Bonding: The shapes and orientations of orbitals determine how atoms interact and bond with each other. For example, the overlap of s and p orbitals in hydrogen and carbon atoms forms covalent bonds in methane (CH₄).
• Electron Configuration: The arrangement of electrons in orbitals (electron configuration) dictates the chemical properties and reactivity of elements. Elements in the same group of the periodic table have similar electron configurations, leading to similar chemical behaviors.
• Spectroscopy: The transitions of electrons between orbitals of different energy levels absorb or emit light at specific wavelengths, providing the basis for spectroscopic techniques used to identify elements and compounds.